An Introduction to Analytical Plane Geometry |
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Common terms and phrases
a² b2 angular points asymptotes Ax+By+C ax² axis bisects centre Chap chord of contact coincide cone conic section conjugate hyperbola constant cos² denote direction directrix distance drawn eccentricity ellipse equal equation for determining Euclid Find the equation Find the locus fixed point foci focus given line given point imaginary inclined infinite intersection latus rectum line at infinity line Ax line joining locus middle point n₂ negative opposite sides parabola Pascal's Theorem perpendicular plane point x'y polar co-ordinates polar equation pole positive projection Prove radius vector ratio rectangular hyperbola represents right angles Similarly sin² straight line tangent theorem touch triangle of reference values vertex x₁ x² y² Y₁ Y₂ zero
Popular passages
Page 105 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 88 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 42 - A point moves so that the difference of the squares of its distances from (3, 0) and (0, — 2) is always equal to 8.
Page 99 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Page 33 - Divide by the square root of the sum of the squares of the coefficients of x and y.
Page 232 - Given four points on a conic, the locus of the pole of a given line is a conic passing through the four points (Chap.
Page 102 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Page 7 - The area of a triangle is equal to half the product of two sides and the sine of the included angle.
Page 182 - If a rectangular hyperbola circumscribe a triangle, the locus of its centre is the
Page 101 - The curve y2 = kqx passes through the origin and the line x = 0 is the tangent at the origin. (Art. 100.) For every positive value of x there are two values of y, equal in magnitude and of opposite sign: thus the curve is symmetrical with respect to the axis of x. Also if x be negative, y is impossible. Thus the curve lies wholly on the Ox side of the axis of y. If x be infinitely great, so is y. Thus the curve is of infinite size. 106. To find the equation to the tangent at the point x'y'.